Hide handles that belongs to non-selected vertices in the bezier curve editor
As far as I know this isn't configurable at the moment.

One possible workaround is to tweak your current theme and dim the colors of unselected handles, or make them closer to say, the world color or viewport background, so they are less visible or intrusive, though they will still actually be visible and selectable.

It is only a workaround, and you have to manually tweak colors for every handle type manually, it would no longer really work once your background color changes, but if you always use the same theme or don't activate the World Background option often, this should not be a problem.